linear function (redirected from Linear functions)

linear function [′lin·ē·ər ′fəŋk·shən]

(mathematics)

linear transformation

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linear function - A recursive function is linear if it is of the form f x = if p x then q x else h f x where h is a "linear functional" which means that (1) for all functions, a, b c and some function ht h (if a then b else c) = if ht a then h b else h c Function ht is known as the "predicate transformer" of h. (2) If for some x, h (\ y . bottom) x /= bottom then for all g, ht g x = True. I.e. if h g x terminates despite g x not terminating then ht g x doesn't depend on g. See also linear argument.